If the no of leaves in a tree is not a power of 2,then the tree is not a binary tree.

(a) How many binary relations are there on a set A with n elements?

(b) How many one - to - one functions are there from a set A with n elements onto itself

State whether the following statement are TRUE or FALSE:
(a) The union of two equivalence relations is also an equivalence relation.

(a) Solve the recurrence equations
$$\,\,\,\,\,\,\,\,\,T\left( n \right) = T\left( {n - 1} \right) + n$$
$$\,\,\,\,\,\,\,\,\,T\left( 1 \right) = 1T$$
(b) What is the generating function?
$$\,\,\,\,\,\,\,\,\,G\left( z \right)$$ for the sequence of Fibonacci numbers?